Recent Applications of the Theory of Lie Systems in Ermakov Systems

We review some recent results of the theory of Lie systems in order to apply such results to study Ermakov systems. The fundamental properties of Ermakov systems, i.e. their superposition rules, the Lewis-Ermakov invariants, etc., are found from this new perspective. We also obtain new results, such...

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Main Authors:	José F. Cariñena, Javier de Lucas, Manuel F. Rañada
Format:	Article
Language:	English
Published:	National Academy of Science of Ukraine 2008-03-01
Series:	Symmetry, Integrability and Geometry: Methods and Applications
Subjects:	superposition rule Pinney equation Ermakov systems
Online Access:	http://www.emis.de/journals/SIGMA/2008/031/

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spelling	doaj-a363327c9d27470197fee8ff278837012020-11-24T23:02:42ZengNational Academy of Science of UkraineSymmetry, Integrability and Geometry: Methods and Applications1815-06592008-03-014031Recent Applications of the Theory of Lie Systems in Ermakov SystemsJosé F. CariñenaJavier de LucasManuel F. RañadaWe review some recent results of the theory of Lie systems in order to apply such results to study Ermakov systems. The fundamental properties of Ermakov systems, i.e. their superposition rules, the Lewis-Ermakov invariants, etc., are found from this new perspective. We also obtain new results, such as a new superposition rule for the Pinney equation in terms of three solutions of a related Riccati equation.http://www.emis.de/journals/SIGMA/2008/031/superposition rulePinney equationErmakov systems
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	José F. Cariñena Javier de Lucas Manuel F. Rañada
spellingShingle	José F. Cariñena Javier de Lucas Manuel F. Rañada Recent Applications of the Theory of Lie Systems in Ermakov Systems Symmetry, Integrability and Geometry: Methods and Applications superposition rule Pinney equation Ermakov systems
author_facet	José F. Cariñena Javier de Lucas Manuel F. Rañada
author_sort	José F. Cariñena
title	Recent Applications of the Theory of Lie Systems in Ermakov Systems
title_short	Recent Applications of the Theory of Lie Systems in Ermakov Systems
title_full	Recent Applications of the Theory of Lie Systems in Ermakov Systems
title_fullStr	Recent Applications of the Theory of Lie Systems in Ermakov Systems
title_full_unstemmed	Recent Applications of the Theory of Lie Systems in Ermakov Systems
title_sort	recent applications of the theory of lie systems in ermakov systems
publisher	National Academy of Science of Ukraine
series	Symmetry, Integrability and Geometry: Methods and Applications
issn	1815-0659
publishDate	2008-03-01
description	We review some recent results of the theory of Lie systems in order to apply such results to study Ermakov systems. The fundamental properties of Ermakov systems, i.e. their superposition rules, the Lewis-Ermakov invariants, etc., are found from this new perspective. We also obtain new results, such as a new superposition rule for the Pinney equation in terms of three solutions of a related Riccati equation.
topic	superposition rule Pinney equation Ermakov systems
url	http://www.emis.de/journals/SIGMA/2008/031/
work_keys_str_mv	AT josefcarinena recentapplicationsofthetheoryofliesystemsinermakovsystems AT javierdelucas recentapplicationsofthetheoryofliesystemsinermakovsystems AT manuelfranada recentapplicationsofthetheoryofliesystemsinermakovsystems
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Recent Applications of the Theory of Lie Systems in Ermakov Systems

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